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# Bijection

From Mathematics Is A Science

Jump to navigationJump to searchA *bijection* is a function that is both

- one-to-one, and
- onto.

In other words, both injective and surjective.

The concept is frequently used to defined equivalence between mathematical structures:

- isomorphism,
- homeomorphism,
- diffeomeorphism, etc.

If there is a bijection $$f:X\rightarrow Y$$ between two set, we say that they have the same cardinality: $$|X|=|Y|.$$